Roxana Barbara Bujack

Classical vector field topology has proven to be a useful visualization technique for steady flow, but its straightforward application to time-dependent flows lacks physical meaning. Necessary requirements for physical meaningfulness include the results to be objective, i.e., independent of the frame of reference of the observer, and Lagrangian, i.e., that the generalized critical points are trajectories. We analyze whether the theoretical concept of distinguished hyperbolic trajectories provides a physically meaningful generalization to classical critical points and if the existing extraction algorithms correctly compute what has been defined mathematically. We show that both theory and algorithms constitute a significant improvement over previous methods.We further present a method to visualize a time-dependent flow field in the reference frames of distinguished trajectories. The result is easy to interpret because it makes these trajectories look like classical critical points for each instance in time, but it is meaningful because it is Lagrangian and objective.

One of the most important properties that inherently defines a good colormap is perceptual order. In the literature, we find a wide range of recommendations and hypotheses regarding order. Properties such as monotonicity in luminance, saturation, or hue are/are not stated as necessary/sufficient to ensure perceptual order. In this paper, we gather the most common statements about perceptual order and, when possible, prove or disprove them.

Color interpolation is critical to many applications across a variety of domains, like color mapping or image processing. Due to the characteristics of the human visual system, color spaces whose distance measure is designed to mimic perceptual color differences tend to be non-Euclidean. In this setting, a generalization of established interpolation schemes is not trivial. This paper presents an approach to generalize linear interpolation to colors for color spaces equipped with an arbitrary non-Euclidean distance measure. It makes use of the fact that in Euclidean spaces, a straight line coincides with the shortest path between two points. Additionally, we provide an interactive implementation of our method for the CIELAB color space using the CIEDE2000 distance measure integrated into VTK and ParaView.

We propose a method for the recognition of vector field patterns under an unknown rotation. The rotation is modeled as a total transformation, which is applied on both spatial coordinates and field values. The invariants are constructed from orthogonal Gaussian-Hermite moments. Their numerical stability and recognition power are shown to be better than those of the invariants published so far.